This brings us to the motivation for considering non-additive IMs. It turns out that IMs whose output is additive cannot be valid. This is the so-called false confidence theorem of [1]}; see, also, [2]}. Demonstrations of the challenges with additive IMs, especially for marginal inference about a function \(\theta =\theta (\omega )\)  of the full model parameter \(\omega \) , can be found in [3]}, [4]}, [5]}, and [6]}, so we will not reproduce the details here. The point is, in order to ensure validity and to enjoy its desirable consequences, it is necessary to consider genuinely non-additive IMs.
